Introduction

The purpose of this article is to describe how to design an efficient flood fill algorithm.

In order to show the strengths of a good design, I must first: describe the basic types of flood filling and there individual strengths and weaknesses.

Note: By efficient, I mean creating an algorithm that reads as few pixels as possible and uses the least amount of memory allocations. Although we are now talking about flood filling a bitmap, historically speaking, flood fills read and wrote directly to the video, which was very slow. Therefore, it was a must to reduce the number of reads and writes; also the amount of memory was limited, so a reduction in memory usage was also a big plus.

What is the QuickFill algorithm?

The QuickFill algorithm is a non-recursive (seed fill) method of filling a 2D graphics image using a scan line search method and doubly linked to lists of nodes to reduce the amount of memory required. The scan line method used in combination with the linked lists, greatly increases the speed at which an image can be filled and allows for multiple fill types to be implemented: background, border, and pattern fills.

Note: The original QuickFill algorithm was written, as part of my personal DOS graphics library, to fill images displayed on a video monitor.

Basic 4 way recursive method

This is the most basic of all flood filling methods, as well as the simplest.

Recursive scan line method

The recursive scan line method is a type of 4 way method, but is more efficient than the 4 or 8 way single pixel recursive methods.

Its strength: complete lines are scanned.

Its weaknesses: repeated sampling of some lines and recursion (may overflow stack).

The diagram above shows how the flooding of a 3x3 image progresses. As you can see: each line was visited 1 to 3 times, and the depth of recursion was 2.

The line fill method below may be inefficient, but it reduces the number of times that a pixel is revisited and reduces the number of recursive calls made. It also has the advantage of being optimizable, that is it can be improved through optimization techniques.

Some techniques that can be applied are:

write scan and search line functions that read and write the image data directly,

The second, so called, optimization technique, appears as if it would slow down the filling process. If it was used in the same way as the stack array in the following code, then you would be correct. The fact is, a linked list allows us to apply other optimization techniques that more than compensate for the slight loss in efficiency. For example: we could pop items off the stack based on there line number, which reduces the number of items on the stack.

Note: Since most programmers now work with bitmaps, instead of reading and writing directly to video, the first optimization above may be all that is required to make this a truly fast solid flood fill algorithm.

The QuickFill algorithm

Finally, we get to the QuickFill method of flood filling, which is a type of 4 way method, but is more efficient than the simple non-recursive method (believe it or not).

Note: For the purposes of this article, I will be describing (mostly) the original QuickFill algorithm, since the included code does not use optimized scan, search, and line drawing functions (remember, the original code directly accessed the video).

Its strengths are:

supports 3 types of fills: background, border and pattern,

optimized scan, search and drawing functions,

no recursion,

use of doubly linked list, to allow for efficiently removing items from list based on line number,

efficient use of list for reverse line splitting, when pattern filling is required.

Its weakness: repeated sampling of some lines, during solid fills.

As you can see from the code below, this is the most complicate method of flood filling. It was derived, indirectly, from the ideas presented in the simple non-recursive method.

The steps taken to create the original code where as follows:

Wrote QuickFill function based on what I could remember about scan line filling.

Replaced stack array with two singly linked lists.

Modified PopLine function, so that lines would be removed based on line number.

Added SearchLeft, SearchRight, ScanLeft, ScanRight functions; in order to allow for optimization of searching and scanning.

Added the PushOpposite function, which reverse splits lines, in order to reduce the number of lines revisited. This required that the list be changed to a doubly linked list and that the list be x-sorted. The reason behind this function was to eliminate all line revisits, but instead it just reduced the number of visits (at a cost).

Optimization of all of the above.

Note: While testing the port of the code to Windows, I discovered a gapping hole in the single visit code, patterns and masks could not be empty or the code would get stuck looping for ever (hence the following).

In order to make this function more useful to Windows programmers, I added code to support flooding of image with a bitmap pattern. Since PushOpposite only reduces the number of lines revisited and does not prevent revisits, I had to add another linked list to keep track of which lines had already been visited. The PushOpposite function is still required as it still reduces the number of line revisits and, as a bonus, it reduces the number of items placed in the visited list. To optimize the visited list, I decided to use visited blocks (rectangles) instead of visited lines, this serves to reduce the number of items needed in the list, which means less memory allocations.

Note: The following is the QuickFill function taken from version 1.0 of the code.

Note: In the following diagram "Scanned" impiles next line to be scanned, when line being pushed is popped off the stack.

Reverse line splitting:

Note: In the following diagram the scanning/pushing starts at the top.

Note: In the following diagram the blue (arrowed) lines represent the lines being pushed.

Background

At the time that the QuickFill algorithm was created, I had seen only two types of flood fills used and wanted an algorithm that could handle both types. The first type used a border-color approach, which meant that the area that needed to be filled first had to be outlined with a border of a given color; this approach is the least desirable of the flood fills. The second type used the color at the seed-point, which meant that only pixels of that color where filled; this approach is much more versatile, since it allows for multiple image objects of varying color to be contained in the area being filled. Both of these flood fill types used a horizontal scan-line approach to solve the problem of flood filling an image.

When trying to find information on how to implement a fast flood fill algorithm, I discovered that there was almost no information on the subject. The only algorithms that I found were:

the basic recursive 4 way flood fill that has been mentioned in many publications (and still is), this is the worst (and slowest) method for filling an image,

a non-recursive scan-line version (ref. 1), that was faster than the 4 way version (still too slow for my purposes), and

a non-recursive scan-line version (ref. 2) that used two linked lists to implement a flood fill algorithm, faster (but still too slow).

The first two methods had the advantage of being very compact, and very slow. The third method on the other hand, had the potential of being very fast and complicated.

After placing the idea on the back burners for a while, since it was for my own personal graphics library and was not a priority, I had an epiphany. I was having a cup of coffee at the local coffee shop and thinking about how I could solve the problem, when it all came together in my head. I started with the ideas used in the simple scan-line algorithm (ref. 1) and proceeded to expand on the idea using a singly linked list (ref. 2) of nodes, representing a LIFO stack. Over the next nine days, I made incremental changes to the algorithm, each designed to increase the over all speed. When I was finished, I had an algorithm that was not only fast, but faster than every implementation that I could find, except for the one implemented in the Fastgraph library by Ted Gruber (written in assembly). Five months after the completion of the code, I finally went back and added the code necessary for single line visits so that the QuickFill function could also handle pattern fills.

References:

Using the code

Note: When running the demo program in slow mode, you can press the ESC key to stop it.

CDibData specific:

If you have not installed the Windows SDK from Microsoft, you will get some compilation errors when compiling in debug mode. The reason for this is that BITMAPV5HEADER was not defined in the SDK that came with Visual C++ 6.0. Since BITMAPV5HEADER is only used for displaying debugging information, it should be easy to comment out the code.

Points of Interest

The code included with this article relies on the CDibData class to provide direct access to bitmap pixels.

I see no barrier to rewriting the code for use with GDI+, the only reason I did not do that, is that, I do not know enough about GDI+ usage at this time. Besides, I have a personal paint program written using GDI and would like to add this code to it.

For those who want to compare the various flood fill algorithms, I suggest the following:

add some tracking variables and code (like the ones in the QuickFill code),

make the test function or functions private members of the QuickFill class,

after the QuickFill initialization, but before the first push, add a call to the test function. Then clean up after the test function call and return without entering the main QuickFill loop.

Note: The above is how I tested the recursive scan line code. Since it was written off the top of my head, I needed to be sure it would work.

If any one knows how to completely eliminate the need for the visited list, I would be very interested. When I discovered that the original method used to reduce revisits did not eliminate them, I felt insulted by my own code. At the time I wrote the QuickFill algorithm, I may have known of this problem and just forgot about it (doubt that).

Question: How would you optimize the QuickFill algorithm for bitmaps?

Answer: Modify the CDibData class so that it has optimized functions for ScanLeft, ScanRight, SearchLeft, SearchRight and horizontal line drawing. Of course, horizontal line drawing would be the hardest, since it would have to work the same as the DrawHorizontalLine member function.

History

Version 1.0

Jan. ??, 2004 : Converted from C (direct video access) to C++ for use with MS Windows bitmaps and added support for: pattern bitmaps to be used as fill and visit-block-list to eliminate revisiting durring pattern & mask fills.

Note: Since the origanal code had direct video access it could take advantage (with the correct write mode) of byte block copping and color-bit-mask reading (read mode 1). Both of which where hardware supported (VGA/EGA monitors) and much more efficeint than reading/writing single pixels directly from/to a bitmap.

Feb. 19, 2004 : Changed internal scan, search and line drawing routines to use pixel color values, in order to increase overall speed while working with palettized bitmaps (modified CDibData).

Mar. 5, 2004 : (1) Moved PushVisitedLine from QuickFill to PushOpposite, this increases the number of revisits and reduces the size of the visit list (8:1). (2) Changed visit list to use HLINE_NODE, since block checking is no longer required and the number of allocations are reduce because the free list can now be used by all. (Of course HLINE_NODE is larger than we need, since it is not a visit list specific node type)

Mar. 9, 2004 : (1) Added argument to QuickFill so that user can specify the rectangular area to be filled. (2) Added the GetInvalidRect function and associated code so that user can retrieve the rectangular coordinates of the bitmap area that has been modified, since lack of this information forces user to redraw whole bitmap.

Changes to demo program:

"Fill Mask" selection option.

"Show Revisits" option. This is used to show which lines were placed in the visit list, when pattern bitmaps or masks are used. Line types: Cyan->line in visit list, Yellow->revisited line direction = -1, Blue->revisited line direction = +1.

Fill area selection via mouse (left-click and drag to select area). To fill: left-click in selected area and release to fill.

Added elapsed fill time and revisit count to information displayed to right of bitmap.

Credits

Andrew J. McCauley for modifying CDibData debug code so that header type checking occurs based on WINVER rather than on header type only. This stopped compilation errors which occurred if the user did not have the new Windows SDK installed.

License

This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.

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About the Author

I am a senior software engineer who has been designing and developing software for many years, mostly in C/C++. You might say that I think in code; which is why I am passionate about my first rule of coding: “First do no harm”. So if I get carried away in my explanations, please realize that it is just part of my personality. I enjoy learning new things and, when I have the time, passing that knowledge onto others.

OK. I got it working by simply correcting a few code errors and adding some new file references to the RecentFileList in the app registry. Oddly, this demo automatically loads the test.bmp but needs the RecentFileList entry to do so.

Also, the test.bmp provided has line breaks everywhere so the whole bmp is always flood filled. I have tested the app with my own bmp that has unbroken line sections and each section fills independently but, as mentioned,does not persist. One would need to save the partially filled bmp in memory to fill different sections with different colors in a persistent manner. Any code to do this greatly appreciated.

Glad you solved the crashing issue, since I have not compiled this for some time. The test application is not met to be useful for anything; other than demonstrating what the algorithm can do. The test bitmap was created specifically to test all possible flooding cases and was instrumental in discovering 1 special case that the original algorithm did not take into account.

I will load this up in Visual Studio 2013 and see if there is anything else wrong.

INTP"Program testing can be used to show the presence of bugs, but never to show their absence." - Edsger Dijkstra"I have never been lost, but I will admit to being confused for several weeks. " - Daniel Boone

From the "QuickFill: An efficient flood fill algorithm" is the following text:

"This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below."

Could you please reply to this post privately so I can ask you a more detailed question about acquiring a license to use the code posted in this article?

I just posted a paper on my website, http://www.crbond.com , which describes in detail a flood fill algorithm which only visits each processed pixel once. It supports filling from other bitmaps, tiles, gradient fills, re-bordering, and flooding under text. I was able to avoid the revisiting problem by processing filled line segments, one at a time, and pushing candidate scan areas on an "up" stack or a "down" stack, depending on which side of the current scan line the adjacent test region was on.

The current version of the description of the flood fill algorithm presented on my website includes a proof that only a single visit of each pixel is possible. To my knowledge, no proof of performance for any other method has been presented in the literature. I welcome comments.

I liked your paper. As far as I can tell, your logic is correct and no revisits would occur. You have even given me an idea, that I cannot remember testing, on how I might fix the revisit problem in my code – if I ever have the time.

And now for the “But” that you knew was coming.

History:

At the time I wrote the original version of the QuickFill algorithm, memory was at a premium and the reduction in stack size was as important as speed. I suspect that the floodfill() in Microsoft's old DOS graphics library may have used a method similar to yours. Microsoft's version choked on one of my solid fill tests and I have always assumed that it just ran out of fixed sized stack space. I cannot remember if it locked up or just returned without finishing the job; I suspect the latter.

Efficiency:

The efficiency of your algorithm is tied directly to the size of your stacks. If they where allocated dynamically, as needed, there would be a drop in efficiency while the stacks where growing. But under normal circumstances, a reasonable initial size, that can grow by a fixed amount - if needed, would help reduce possible memory allocation [and copy] hits.

The reason I bring up memory allocation, as opposed to a fixed stack size, is that the size of the stacks required by your algorithm could be quite large. In the test I mentioned above, the number of segments that could be pushed on the stack was in the hundreds, if not more. That is why that method was rejected during the design of the QuickFill algorithm – it did not meet efficient memory usage requirements.

The Test:

If I remember correctly, I created a very large image filled with U shaped boxes, at least 3x2 pixels, spaced 1 or 2 pixels apart. Then set the fill point (seed point) at bottom to see what happened.

I believe this, or something similar, would be a good test for your algorithm, as every one of the openings to each of those boxes will be pushed onto the fill down stack before fill_up() is finished.

Any way, thanks for the post, I found it educational.

- John R. Shaw

INTP"Program testing can be used to show the presence of bugs, but never to show their absence." - Edsger Dijkstra"I have never been lost, but I will admit to being confused for several weeks. " - Daniel Boone

Thanks for the response. Regarding the memory efficiency vs. other considerations, I guess it's too much to expect one algorithm to achieve everything. Anyway, I've written a test program which monitors the pixel visits, stack sizes, etc., and hope to expand the paper to disclose everything I've found. Ideally, a potential requirement for flood fill methods could order the priorities in a way that makes the final selection of a method fairly straightforward.

When I revise the paper to include test data, I'll forward a link to you.

Perhaps I misunderstand something, but consider the following fill beginning at 1, where the numbers are fillable and the Xs aren't:

X X X X X
X 234 X
X 1 X 5 X
X 876 X
X X X X X

As I understand it:1 would be filled and 8 would be pushed on the down stack.234 would be filled and 5 would be pushed on the down stack.Since the top boundary is reached, 5 would be popped and a down scan begun.5 would be filled.678 would be filled and 1 would be pushed on the up stack.Since the bottom boundary is reached, 1 would be popped and an up scan begun.1 would be revisited.Since 1 is already filled, 8 would be popped and a down scan begun.8 would be revisited.The fill would be complete since 8 is already filled and the stacks are empty.